Nanofluid PCMs for thermal energy storage: Latent heat reduction mechanisms and a numerical study of effective thermal storage performance

Nanofluid PCMs for thermal energy storage: Latent heat reduction mechanisms and a numerical study of effective thermal storage performance

International Journal of Heat and Mass Transfer 78 (2014) 1145–1154 Contents lists available at ScienceDirect International Journal of Heat and Mass...

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International Journal of Heat and Mass Transfer 78 (2014) 1145–1154

Contents lists available at ScienceDirect

International Journal of Heat and Mass Transfer journal homepage: www.elsevier.com/locate/ijhmt

Nanofluid PCMs for thermal energy storage: Latent heat reduction mechanisms and a numerical study of effective thermal storage performance Aitor Zabalegui, Dhananjay Lokapur, Hohyun Lee ⇑ Mechanical Engineering, Santa Clara University, CA, 500 El Camino Real, Santa Clara, CA 95053, United States

a r t i c l e

i n f o

Article history: Received 7 February 2014 Received in revised form 13 June 2014 Accepted 17 July 2014 Available online 15 August 2014 Keywords: Nanofluid Phase change materials Thermal energy storage

a b s t r a c t The latent heat of fusion of paraffin-based nanofluids has been examined to investigate the use of enhanced phase change materials (PCMs) for thermal energy storage (TES) applications. The nanofluid approach has often been exploited to enhance thermal conductivity of PCMs, but the effects of particle addition on other thermal properties affecting TES are relatively ignored. An experimental study of paraffin-based nanofluids containing various particle sizes of multi-walled carbon nanotubes has been conducted to investigate the effect of nanoparticles on latent heat of fusion. Results demonstrated that the magnitude of nanofluid latent heat reduction increases for smaller diameter particles in suspension. Three possible mechanisms – interfacial liquid layering, Brownian motion, and particle clustering – were examined to explain further reduction in latent heat, through the weakening of molecular bond structures. Although additional research is required to explore detailed mechanisms, experimental evidence suggests that interfacial liquid layering and Brownian motion cannot explain the degree of latent heat reduction observed. A finite element model is also presented as a method of quantifying nanofluid PCM energy storage performance. Thermal properties based on modified effective medium theory and an empirical relation for latent heat of fusion were applied as model parameters to determine energy stored and extracted over a given period of time. The model results show that while micro-scale particle inclusions exhibit some performance enhancement, nanoparticles in PCMs provide no significant improvement in TES performance. With smaller particles, the enhancement in thermal conductivity is not significant enough to overcome the reduction in latent heat of fusion, and less energy is stored over the PCM charge period. Therefore, the nanofluid approach may not be justifiable for energy storage applications. However, since the model parameters are dependent on the material properties of the system observed, storage performance may vary for differing nanofluid materials. Ó 2014 Elsevier Ltd. All rights reserved.

1. Introduction Thermal energy storage (TES) based on phase change phenomena is promising for sustainable thermal power generation and residential heating, due to the high specific storage capacity of phase change materials (PCMs). However, the characteristically low thermal conductivity of PCMs limits the rate at which they can exchange thermal energy with other heat transfer media. Due to this low charge/discharge rate, PCMs in TES applications may not meet the energy demand over given periods of time, and thus, will require larger heat exchangers. Several methods have been proposed to enhance heat transfer rates of PCMs. Wu et al. [1] and ⇑ Corresponding author. Tel.: +1 408 554 5283. E-mail address: [email protected] (H. Lee). http://dx.doi.org/10.1016/j.ijheatmasstransfer.2014.07.051 0017-9310/Ó 2014 Elsevier Ltd. All rights reserved.

Zhang et al. [2] suggested micro and nano-encapsulation of PCMs to increase the surface area to volume ratio, while Fukai et al. [3] and Velraj et al. [4] suggested structural modifications to thermal storage systems, such as the addition of fin configurations and the insertion of a metal matrix. The nanofluid approach, involving the dispersion of high conductivity particles into a base fluid, has also been demonstrated as an effective way of enhancing thermal conductivity, although the mechanisms behind it are controversial [5,6]. An advantage of the nanofluid approach is its ability to be combined with the previously mentioned structural modifications to further augment heat transfer efficiency. Theoretical and experimental studies by Prasher et al. [7] and Gao et al. [8] have identified nanoparticle clustering effects as the determining factor for nanofluid conductivity enhancement. Furthermore, modified effective medium theory (EMT) by Nan et al. [9,10] considers high

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nanoparticle aspect ratio and Kapitza resistance, and shows good agreement with reported values. Although considerable research efforts have focused on nanofluid thermal conductivity, other thermal properties affecting TES, such as specific heat capacity or latent heat of fusion, do not receive as much attention. Specific heat capacity is commonly believed to exhibit no nanoscale effects [11], but recent experimental findings by Shin and Banerjee [12,13] and Wang et al. [14] show significant heat capacity enhancement in nanostructures and nanofluids. Shin and Banerjee proposed that the observed nanofluid heat capacity enhancement was due to improved thermal properties of semi-solid layers at particle interfaces, formed by liquid layering effects. On the other hand, nanofluid latent heat of fusion is expected to linearly decrease as particles not contributing to phase change are added to the base fluid [15,16]. However, several experimental studies on nanofluids have reported additional reduction beyond latent heat EMT. Wu et al. [15] reported a nearly 10% drop from the expected latent heat of Cu/paraffin nanofluids with 25 nm diameter particles at 1% volume fraction. Zeng et al. [17] observed a similar reduction at 1% volume fraction with copper nanowires in tetradecanol. Ho and Gao [18] reported a less significant reduction of approximately 3% for alumina-in-paraffin emulsions, with 177.8 nm diameter particles at 2% volume fraction. Despite the similarity of these observations and their inconsistency with theory, latent heat characterization was not the intended focus of these studies. Although no possible reduction mechanisms were suggested, Wu et al. [15] proposed that a new model for latent heat EMT of solid–liquid mixtures is needed. From the reported findings, it is apparent that nanofluids of smaller particle diameter exhibit greater reduction in latent heat of fusion. Studies to investigate this relationship have yet to be conducted. Since most TES applications require energy to be stored or released in a given amount of time, storage performance can be evaluated as how much energy is transferred over a given duration. Both latent heat of fusion and thermal conductivity affect energy storage performance. While enhanced thermal conductivity improves the rate of heat transfer, reduced latent heat decreases specific energy storage capacity. Although reduced latent heat can also increase energy charge/discharge rates due to shortened melt time, greater nanofluid PCM volume will be required to account for reduced storage capacity. Without reliably quantifiable thermal properties, the nanofluid approach may not be effective for PCM thermal energy storage. In this work, a comprehensive characterization study of nanofluid latent heat of fusion has been conducted. Possible reduction mechanisms are explored with respect to measured results. In addition, a numerical model of nanofluid phase change is presented as a predictive tool to determine the amount of energy stored/extracted in a given amount of time. Applying nanofluid thermal conductivity enhancement approximated by Nan’s EMT, the proposed numerical model serves as a predictive tool to determine the effects of the diameter-dependent latent heat reduction observed.

(STA 449 F3 Jupiter, NETZSCH). More details about the sample preparation and experimental method were presented in our previous work [19]. An optical microscope (SMZ1500, Nikon) was utilized to examine suspension stability, since the surface charge accumulation caused by non-conductive paraffin hinders imaging with electron microscopy. No significant change in the degree of nanoparticle clustering was observed before and after melt cycling. In addition, no observable sedimentation occurred for stock left in liquid state on a hot plate over a five-day period. Another vial of stock underwent phase transition cycling over the same five-day period. The stock was melted twice per day and left in liquid state for at least two hours at a time. No visible sedimentation was detected. 3. Characterization results and discussion Differential Scanning Calorimeter (DSC) measurements show that at each volume fraction tested, sample latent heat of fusion reduces for nanofluids of smaller particle diameter. At 1% particle volume fraction, nanofluids with 15.5 nm diameter MWNTs exhibit an additional 10% reduction below the mass loss prediction. Shown in Fig. 1, all samples exhibit linear latent heat reduction with particle loading, below that expected by traditional EMT. Looking at a single volume fraction, latent heat is observed to reduce with smaller diameter particles in suspension. Therefore, additional reduction below the mass loss prediction is shown to be independent of particle volume fraction. The apparent diameter-dependence suggests that interface effects may have a role in nanofluid latent heat reduction. Defining r as latent heat reduction rate with respect to particle volume fraction, Fig. 1 shows that the magnitude of reduction rates increases as particle diameter decreases. Several experimental studies also appear to follow this trend [15,17,18]. However, the nanofluids investigated by both Wu et al. and Ho and Gao contain spherical particles, which may explain observed differences from the measured results. An average value was estimated from provided SEM images of the work by Zeng et al., which may not serve as an accurate representation. Nevertheless, the strong dependence on particle diameter suggested by these results serves as a basis for assessing the contributions of the proposed latent heat reduction mechanisms. Theoretically, the latent heat of fusion of composite materials is expected to linearly decrease with particle addition,

2. Sample preparation and experimental method Multi-Walled Nanotubes (MWNTs) of 15.5, 40, 65, and 400 nm outer diameter (Cheap Tubes Inc.) were dispersed in liquid paraffin (126 MP Wax – 3032, Candlewic) at 0.2%, 0.5%, and 1.0% particle volume fractions, using high frequency pulse sonication (VCX750 Ultrasonic Processor, Sonics & Materials, Inc.). Once mixed, stock nanosuspensions were individually poured into an acrylic mold, solidified, and cut into 12  12 mm samples. Sample latent heat of fusion was measured using differential scanning calorimetry

Fig. 1. Normalized nanofluid latent heat of fusion versus particle volume fraction measured by DSC, along with experimental works by other groups. At constant particle volume fractions, nanofluid latent heat is shown to reduce with decreasing particle size.

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hsl;nf ¼

qbf ;s hsl;bf ð1  /p Þ ; qnf

ð1Þ

where qbf,s denotes the base fluid density in solid phase, qnf is the theoretical nanofluid density, and hsl,bf is the solid–liquid latent heat of the base fluid. As mentioned previously, nanofluid latent heat reduction is defined by the mass – or volume – of particles within the nanofluid that does not contribute to phase change. In accordance with experimental findings, latent heat reduction beyond the mass loss prediction suggests that aside from nanoparticle volume, there is additional volume not contributing to latent heat. It is proposed that this additional volume is represented by effective volumes of strained base fluid molecular structure, which require less energy to break down during melting. Molecular strain may be attributed to the following interfacial phenomena: interfacial liquid layering, Brownian motion, and particle clustering. Each of these effects is diameter-dependent, and has a greater impact with reduced particle size. Therefore, these phenomena are considered as mechanisms for the diameter-dependent nanofluid latent heat reduction observed. The contribution of each reduction mechanism is analyzed by approximating the respective strained region volume generated, and comparing it to the strained volume required to explain observed reduction. 3.1. Interfacial liquid layering The first mechanism, interfacial liquid layering, facilitates latent heat reduction through the weakening of base fluid molecular structure. At the interface, van der Waals forces attract nearby base fluid molecules, forming a more ordered and densely packed layer. During this process, molecular bonds between surrounding base fluid molecules are strained, and require less energy to break down during melting. The effects of strain propagate normal to the interface, as the inverse of distance from the particle surface. Since the number density of layered molecules increases with interface density, smaller diameter particles generate greater volumes of strained regions. To consider this effect theoretically, interface volume fraction (/i) is defined as the volume of interface phase (Vi) – including both the densely packed layer at the interface and surrounding strained layer – over the total nanofluid volume (Vnf).

/i ¼

Vi V nf

ð2Þ

Representing total nanofluid volume as a function of particle volume and particle volume fraction, Eq. (2) can be expressed as:

 /i ¼ /p

Vi Vp

 ð3Þ

where / is volume fraction, with i and p subscripts denoting interface and particle, respectively. Interface and particle volumes can be expressed through geometric functions of particle diameter (dp), length (L), and interface phase width (w), as shown in Fig. 2.

0

pL B

/i ¼ /p B @



dp 2

2  2 1 d ! þ w  2p C 4w 4w2 C  2 A ¼ /p dp þ 2 dp pL d2p

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ð4Þ

After simplification, Eq. (4) demonstrates that interface volume fraction is inversely proportional to particle diameter when w/dp is much less than unity. It has been established from both experimental studies and molecular dynamics simulations that the width of the densely packed layer (DPL) is no more than 1–2 nm [20,21]. Since attractive forces dissipate normal to the particle surface, base molecules further away from the interface migrate shorter distances. The DPL

Fig. 2. Cross-section of MWNT with diameter dp, surrounded by a densely packed layer and strained layer of base fluid molecules, with a collective interface phase width w.

width is thin (on the order of molecular spacings), demonstrating that the effect of van der Waals forces is relatively weak. Therefore, base molecules beyond the DPL do not experience significant movement, and the total interface phase width should scale on the same order as the DPL width. Consequently, interface volume fractions should also scale similarly to effective interface volume fractions consisting of only the DPL. Interface volume fractions for each particle size tested can be evaluated from measured nanofluid latent heat, using a modified mass loss prediction for a ternary system. The nanofluid ternary system consists of the base fluid, nanoparticles, and interface phase. As a minimum estimate of interface volume fraction, interface phase structure is assumed to be completely broken down and not contributing to latent heat:

hsl;nf ;tern ¼

qbf ;s hsl;bf ð1  /p  /i Þ qnf

ð5Þ

Using Eq. (5), interface volume fractions required to fit measured nanofluid latent heat are calculated and summarized in Table 1, for all particle diameters tested. DPL volume fractions are also calculated, using Eq. (4), assuming a DPL width of w = 2 nm. In Table 1, all interface volume fractions are shown normalized by particle volume fraction, and thus, are represented as ratios of either interface phase or DPL volume to individual particle volume. Also included are MWNT geometries and the required width of the interface phase to fit measured reduction, calculated from Eq. (4). The resulting required interface volume fractions significantly overestimate interface volume fractions consisting of only the DPL. Corresponding required interface phase widths are on the order of particle diameter, which is highly inconsistent with approximations in literature [22]. Since strained regions within the interface phase are unlikely to occupy volumes two orders of magnitude greater than respective DPL volumes, interfacial layering effects cannot solely explain the degree of latent heat reduction observed. A correlation between interfacial liquid layering and measured latent heat can be made, considering the inverse proportionality to particle diameter in Eq. (4). As shown in Fig. 3(a), each particle diameter independently shows a linear relation to latent heat reduction, but a weaker fit is demonstrated (r = 0.8625) when considering all particle diameters tested. Alternatively, a very strong correlation (r = 0.9729) among all particle diameters is seen in Fig. 3(b), considering proportionality to the inverse square root of particle diameter. Proportionality to the inverse square root of particle diameter was originally considered because it describes

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Table 1 Interface volume fractions required to fit measured nanofluid latent heat for all particle sizes tested (Vi,req/Vp), calculated with Eqs. (3) and (5). Required interface volume fractions are compared to effective interface volume fractions consisting of a 2 nm thick densely packed layer (Vi,DPL/Vp). Interface volume fractions are normalized by particle volume fraction (/i//p), and represented as ratios of interface volume to particle volume. MWNT diameter [nm]

MWNT length [lm]

MWNT aspect ratio

w required to fit hsl,nf [nm]

Vi,req/Vp

Vi,DPL/Vp

15.5 40.0 65.0 400.0

6.5 15.0 15.0 27.5

419.4 375.0 230.8 68.9

17.5 39.0 50.0 125.0

9.62 7.69 5.44 1.65

0.58 0.21 0.13 0.02

Fig. 3. Normalized nanofluid latent heat versus functions of particle diameter. (a) Plotted versus inverse particle diameter, representing interfacial liquid layering, with a correlation coefficient, r = 0.8625. (b) Plotted versus inverse square root particle diameter, a proportionality of Brownian diffusion, with r = 0.9729.

the diameter-dependency of particle diffusion due to Brownian motion. The strong correlation between this proportionality and observed latent heat reduction suggests that Brownian motion may have a significant role as a reduction mechanism. Another important parameter to note in Table 1 is the aspect ratio of the samples tested. Aspect ratio decreases from approximately 420 for the 15.5 nm diameter nanoparticles to 69 for the 400 nm nanoparticles. Consequently, these aspect ratios also show an inverse proportionality to the square root of particle diameter. The mutual proportionality of particle aspect ratio and observed latent heat reduction implies not only a direct correlation, but also that potential reduction mechanisms should be highly dependent on aspect ratio. 3.2. Brownian motion Brownian movement facilitates latent heat reduction by causing a disruption of base fluid molecular structure as nanofluids undergo phase change. The random movement of nanoparticles in the medium results in an effective sweep volume of weakened bond structure that requires less energy to breakdown during phase change, and may account for the additional volume not contributing to latent heat. By calculating average Brownian diffusion length, k, the sweep volume generated by a single particle in suspension can be estimated. The magnitude of this Brownian sweep volume can be compared to the equivalent interface phase volume, Vi,req, required to fit measured nanofluid latent heat reduction – found using Eqs. (3) and (5). If both volumes are on the same order of magnitude, Brownian movement can theoretically account for latent heat reduction not explained by liquid layering effects. The range of Brownian sweep volumes for cylindrical particles is at a minimum when diffusion is solely in the axial direction, and

maximum when solely in the radial direction. The range of Brownian sweep volumes can be expressed as a function of average Brownian diffusion length, assuming a 2 nm thick interface phase width:

" 2  2 #  2 dp dp dp þ pk pL þw  þ w 6 V BrS 2 2 2 " 2  2 # dp dp þ kLðdp þ 2wÞ 6 pL þw  2 2

ð6Þ

For Brownian motion in the diffusive regime, average Brownian diffusion length, k [m], is inversely proportional to the square root of particle diameter,

pffiffi k¼ t

sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2kB T 3pldp

ð7Þ

where l is dynamic viscosity, t is the time scale, kB is the Boltzmann constant, and T is the absolute temperature. The time scale for Brownian diffusion is of the same order of magnitude as momentum relaxation time [23]. For a particle of mass m, momentum relaxation time is given as:

sp ¼

mp 6pldp

ð8Þ

Instead of approximating Brownian sweep volumes, required Brownian diffusion times to explain observed latent heat reduction can be estimated and compared to respective momentum relaxation times. Axial and radial Brownian sweep volumes were fit to required interface phase volumes, Vi,req, to calculate required average diffusion length (Eq. (6)). Required diffusion lengths were applied to Eq. (7) to calculate ranges of required diffusion times.

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Fig. 4. Approximate time scales required for axial and radial Brownian sweep volumes of various diameter MWNTs to explain observed latent heat reduction, compared to respective momentum relaxation time scales.

A comparison of the resulting time scales is shown in Fig. 4, demonstrating that required diffusion time scales are two orders of magnitude larger than the momentum relaxation time. Thus, the time scale for Brownian motion is too slow to explain the additional reduction in nanofluid latent heat of fusion. 3.3. Particle clustering Particle aggregation into high aspect ratio clusters has been described as the key mechanism for nanofluid thermal conductivity enhancement [7,22,24]. Percolation effects due to direct contact between aggregated particles explain thermal conductivity enhancement beyond traditional Maxwell theory. The effective volume of an aggregate cluster is larger than the volume of nanoparticles within the cluster, and exhibits higher thermal conductivity than the base fluid. Keblinski et al. state that even for densely packed aggregates, roughly 25% of cluster volume is occupied by base fluid filling the voids between particles. Aggregates are formed as a result of inter-particle attraction due to van der Waals forces. It is proposed that base fluid structure is strained as particles migrate towards each other. Similar to Brownian motion, the clustering or movement of particles in the medium weakens bond structure, leading to a reduction in latent heat. Strained base fluid volume within aggregate clusters can account for the interface volume required to explain observed latent heat reduction. As described by Prasher et al. [7,24], aggregates are characterized by their radius of gyration (Ra). Radius of gyration is defined as the root mean square of the average radius from the cluster’s center of mass. Prasher et al. define /int as the volume fraction of particles within aggregate clusters, and /a as the volume fraction of aggregates in the nanofluid. Hence, particle volume fraction can be defined as

/p ¼ /int /a

ð9Þ

For a completely dispersed nanofluid, /int = 1 and /p = /a, since each aggregate is composed of a single particle. On the other hand, /a = 1 and /int = /p for a completely aggregated nanofluid, since the entire nanofluid volume is composed of a single aggregate cluster. The volume fraction of particles within formed clusters, /int, is given by Potanin and Russel [25]:

/int ¼ ð2Ra =dp Þ

df 3

ð10Þ

where df is the fractal dimension of the aggregates, ranging from 1.75 to 2.5 [7]. Prasher et al. [7] assume df = 1.8, based on observations by Wang et al. [26] showing that nanofluids exhibit diffusionlimited cluster–cluster aggregation (DLCCA). Low range fractal dimensions represent a weak repulsive barrier, which is characteristic of DLCCA. To investigate particle clustering’s maximum potential contribution to latent heat reduction, ratios of maximum effective cluster volume to particle volume can be estimated, assuming a completely aggregated nanofluid. Since cluster volumes include the volume of particles within the cluster, maximum cluster volume ratios should be compared to the following ratio:

V iþp;req V i;req þ V p ¼ Vp Vp

ð11Þ

Eq. (11) is a more appropriate comparison than the required interface volume fractions in Table 1, which do not include particle volume. Since /a = 1 for a fully aggregated nanofluid, Eq. (9) can be reduced to /int = /p. Thus, the maximum cluster radius of gyration is given by:

ðRa Þmax ¼ ðdp =2Þð/p Þ1=ðdf 3Þ

ð12Þ

where /int in Eq. (10) has been replaced with particle volume fraction, /p. Assuming spherical clusters, calculated values of (Ra)max at various particle volume fractions allow for the estimation of maximum cluster volumes, (Va)max. As seen in Fig. 5, resulting maximum cluster volumes, normalized by particle volume, are orders of magnitude larger than required interface volume fractions (Eq. (11)). Required interface volume ratios from Table 1 are normalized by particle volume; and thus, are well-represented by a power function trend line of the form Vi,req/Vp = C(dp)1/2. On the other hand, maximum cluster volume ratios are shown for several particle volume fractions. Cluster volume ratios demonstrate linear fit with respect to diameter, as they describe a spherical to cylindrical volume ratio. Trend line approximations show that smaller particle volume fractions produce greater cluster volume fractions. Cluster volume fractions are shown to increase with larger particle size, producing a greater divergence from required interface volume fraction. Despite these trends, larger particles at smaller volume fractions are less likely to aggregate.

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Fig. 5. Ratios of maximum aggregate volume to particle volume for various particle volume fractions, with respect to particle diameter. Maximum aggregate volume is calculated assuming a spherical cluster of radius (Ra)max (Eq. (12)). Volume ratios are compared to interface volume fractions required to explain latent heat reduction, normalized by particle volume fraction (Eq. (11)).

Although the effect of strain within aggregate clusters is not considered in Fig. 5, the approximated scale of cluster volume fractions suggest that clustering is the principal mechanism for nanofluid latent heat reduction. Exact cluster volume fractions required to fit required interface volume fractions can also be calculated, providing an estimate of the necessary degree of aggregation within the nanofluid. Firstly, the effective radius of volume Vi+p,req is calculated and substituted into Eq. (10), in place of the cluster radius of gyration. Lastly, resulting values of /int are used in Eq. (9) to calculate required cluster volume fraction. These values are provided in Fig. 6, normalized by particle volume fraction, and are also well-described by the inverse square root of particle diameter. Fig. 6 shows that cluster volume fraction must be at least an order of magnitude larger than particle volume fraction to account for the latent heat reduction observed.

Ultimately, additional research efforts are needed to further investigate particle clustering as a latent heat reduction mechanism. Direct measurement of nanofluid thermal conductivity, for example, will allow for the estimation of cluster volume fraction using Prasher’s method [7,27]. Approximations of cluster volume fraction can be compared to ratios provided in Fig. 6. In addition, molecular dynamics simulation should be conducted to provide a clearer understanding of the proposed reduction phenomena. According to the strong correlation demonstrated in Fig. 3(b), observed latent heat reduction is well-described by a dependency on the inverse square root of particle diameter. This relationship was the basis for considering Brownian motion as a reduction mechanism. As shown in previous work [19], the volume ratios Vi,req/Vp in Table 1, defined as required interface volume fraction normalized by particle volume fraction, can be described by a power function trend line of the form Vi,req/Vp = C(dp)1/2. Thus, strained phase volume over particle volume may be considered approximately proportional to the inverse square root of particle diameter. By using this power function to calculate required interface volume fraction, Eq. (5) may be used to approximate nanofluid latent heat of fusion. Regardless of the underlying mechanisms for further reduction in latent heat of fusion, the empirical relation presented can be used to identify the validity of the nanofluid approach for TES. Since the developed nanofluids are intended for use in TES applications, it is important to consider the effects of change in thermal properties on TES performance.

3.4. Numerical study of nanofluid PCM thermal storage performance

Fig. 6. Minimum cluster volume fraction to particle volume fraction ratios required for particle clustering to explain observed latent heat reduction, with respect to particle diameter. Approximated ratios scale proportionally with particle volume fraction, and are well-described by a power function trend line of the form /a,req//p = C(dp)0.5.

In our previous work [19], nanoparticle size is shown to have a much greater impact on latent heat than thermal conductivity. In short, a smaller particle diameter leads to a slight increase in thermal conductivity and a significant reduction in latent heat, suggesting that greater volumes of nanofluid PCM can be melted in a given period of time by reducing particle size. However, reduction of latent heat will decrease the amount of energy stored per unit mass. These counteracting effects complicate the quantitative assessment of nanofluid energy storage performance. A numerical model has been developed to determine the optimum particle diameter and volume fraction to maximize the

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amount of heat transferred over a given period of time. In accordance with our experimental findings, the numerical model incorporates values for nanofluid latent heat of fusion that consider additional volume not contributing to phase change. Specifically, the empirical relation for nanofluid latent heat given in Fig. 6 is applied to Eq. (5) to provide approximate values for the model. The numerical model presented in this paper simulates transient nanofluid phase change in an annular storage container. PCM in the outer annulus is heated convectively by a working fluid in the inner annulus, while the outside of the container is insulated and cooled by the surrounding air. Conduction heat transfer within the annulus is assumed to be axially symmetric, and thus, can be modeled as one-dimensional. Convection within the PCM is neglected. The model incorporates a finite element approach, based on the enthalpy method [27]. The enthalpy method solves for stored internal energy at individual nodes at each time step, determines the phase of the material accordingly. Fig. 7 shows the configuration of nodes within the annulus, along with the control volumes used to derive discretized equations for both the inner nodes and boundary conditions. Nodes are spaced at Dr steps, and range from ro (j = 1) at the heated interface to rN (j = N) at the container wall. All discretized equations are derived from the first law of thermodynamics, neglecting work done due to PCM expansion during phase change.

  1 @ @T dT ¼ qc kr r @r @r dt

ð13Þ

The total enthalpy in solid and liquid state is defined as:

8R < T melt qcs dT; for T E ¼ R Tinit R T final : melt qc dT þ for s T melt qc l dT þ qhsl ; T init

T < T melt T > T melt

ð14Þ

where subscripts init and final denote initial and final states, and Tmelt signifies melting temperature. In discretized form, solid and liquid state enthalpies are defined as:

8   > < qcs T ij  T i ; for     Eij ¼ > : qcs T ij  T i þ qcl T ij  T m þ qhsl ; for

T ij < T melt T ij > T melt

ð15Þ

A discretized equation for the enthalpy at inner nodes [j = 2 to j = (N  1)] is derived from the first law, considering the control volume (CV) in Fig. 7(b). Applying an energy balance, conduction into the CV is equal to the sum of internal energy and conduction out of the CV. The discretized form of this energy balance is given by:

q00cond r ð2pr j1=2 LÞ  q00cond rþDr ð2prjþ1=2 LÞ ! h  i T iþ1  T i j j i 2 2 ¼ qcj pL r jþ1=2  r j1=2 Dt

ð16Þ

where subscripts r and j signify radial and nodal position, respectively, and superscript i is the iterative time step, initially at i = 1. Since the surface area at each node increases moving outward from

Fig. 7. (a) Configuration of nodes within annular PCM storage container, at initial temperature TPCM,init, heated convectively by a working fluid at constant temperature T1,wf. Nodes range from ro (j = 1) at the heated interface to rN (j = N) at the container wall, spaced apart by Dr steps. (b) Control volume defined to derive the discretized governing equation for the enthalpy at inner nodes [j = 2 to j = (N  1)]. (c & d) Control volumes defined to derive discretized boundary conditions for the enthalpy at (c) the heated interface (j = 1) (d) storage container wall (j = N).

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the center of the annulus, the radius at each node must be considered. The conduction terms in Eq. (16) may be represented by Fourier’s law for one-dimensional conduction: i

kj1=2 ð2pr j1=2 LÞðT j1  T j Þ

Dr

i

þ

kjþ1=2 ð2pr jþ1=2 LÞðT j  T jþ1 Þ

h

 i T iþ1  T i j j ¼ qcij pL r 2jþ1=2  r 2j1=2 Dt

!

Dr ð17Þ

Distributing qc within the time derivative, the term on the right hand side can be expanded in order to combine qcT terms as discretized enthalpy terms, as defined in Eq. (15).







qcj T iþ1  qcj T i þ qcj T i  qcj T ij j



Dt

¼ Ejiþ1  Eij

ð18Þ

Squared radius terms at half nodes can also be expanded:

      Dr 2 Dr 2 r 2jþ1=2  r 2j1=2 ¼ r j þ  rj  ¼ 2r j Dr 2 2

ð19Þ

and shown to reduce to the simple expression, 2rjDr. By incorporating the simplified expressions of Eqs. (18) and (19) into Eq. (17), dividing out by pL and 2rjDr, and rearranging terms, the final form of the governing discretized equation for the enthalpy at inner nodes is given as:

" Eiþ1 j

¼

Eij

þ "



Dt

rj ðDrÞ

Dt

#   i kj1=2 r j1=2 T ij1 2

#   i i kjþ1=2 r jþ1=2 þ kj1=2 r j1=2 T ij 2

r j ðDrÞ " #  Dt  i T ijþ1 þ k r jþ1=2 jþ1=2 r j ðDrÞ2

ð20Þ

Discretized enthalpy equations at the heated interface j = 1 and container wall j = N are derived from boundary conditions matching conduction and convection. An energy balance is applied to each of the CVs in Fig. 7(c) and (d). Starting with Fig. 7(c), the appropriate energy balance is:

    ki1þ1=2 ð2pr 1þ1=2 LÞ T i1  T i2 U i ð2pr1 LÞ T 1;wf  T i1  Dr  3 2  n pL r21þ1=2  r21 T nþ1  T 1 1 5 ¼ qc 1 4 Dt

ð21Þ

By using the same methods of simplification in Eqs. (18) and (19), Eq. (21) can be expressed in its final discretized form:

"

Eiþ1 1

!# i k1þ1=2 r1þ1=2 2 Dt T i1 ¼  2 U i r1 þ Dr r1þ1=2  r 21 2 3 " # i 2k1þ1=2 r 1þ1=2 Dt i 2U i r 1 Dt 4 5   T2 þ 2 Ti þ r 1þ1=2  r 21 1;wf Dr r 21þ1=2  r21 Ei1

ð22Þ

To derive the discretized boundary condition at the container wall, the energy balance for the control volume in Fig. 7(d) is given as:

  i kN1=2 ð2prN1=2 LÞ T iN1  T iN

   U o ð2pr N LÞ T iN  T 1;air    qcN pL r2N  r2N1=2 T Niþ1  T iN

Dr

¼

Dt

and the final discretized equation takes the form:

ð23Þ

Eiþ1 1

¼

Ei1

þ "

" i # 2kN1=2 r N1=2 Dt

Drðr2N  r2N1=2 Þ i

T iN1

kN1=2 r N1=2 2Dt  2 þ U o rN Dr r N  r 2N1=2 " # 2U o r N Dt Ti þ 2 r N  r 2N1=2 1;air

!# T iN ð24Þ

Solved enthalpy values at each node and iterative time step are used to solve for temperatures, liquid volume fraction k, and thermal conductivity at the following time step. Table 2 provides a summary of the appropriate equations to estimate these properties, given different ranges of solved enthalpy values. Liquid volume fraction is zero when the material is in solid state, and 1 when in liquid state. When the temperature of the material has reached melting point, the material enters a ‘‘partial mush’’ state. In this mush state, the liquid volume fraction is defined as the fraction of stored enthalpy over the enthalpy required for the material to fully melt. Therefore, liquid volume fraction is an indicator of the material’s state, and its progress towards melting during phase change. Equations for temperature were derived from Eq. (15). Thermal conductivity in the particle mush state is taken from Alexiades and Solomon [27], signifying a ‘‘sharp front’’ melting interface, with layers of solid and liquid in a serial arrangement. Model parameters were chosen by considering a nanofluid PCM of CNT particles dispersed in paraffin wax. The physical and thermal properties of multi-walled carbon nanotubes and paraffin wax are shown in Table 3. These values are used to approximate effective nanofluid thermal conductivity using Nan et al.’s model. An empirical relation of aspect ratio to particle diameter, taken from the nanoparticles tested, was applied for other particle sizes modeled. Initially, the temperature of the wax is assumed to be uniform throughout the container, at 293 K. The temperature of the heat source (the working fluid) is 358 K, with an overall heat transfer coefficient (Ui) of 3000 W/m2 K, and the surrounding air temperature is 293 K, with an overall heat transfer coefficient (Uo) of 1 W/m2 K. The inner and outer radii of the annulus are 1 and 5 cm, respectively. Using the above parameters, a storage container of pure paraffin undergoing an 8 h charge period was modeled at 0.1 s time intervals. The temperature distribution along the radius of the cylinder at 2, 4, 6, and 8 h is shown in Fig. 8(a). The horizontal line on the plot represents the melting temperature of pure paraffin (326 K). A distinct change in the temperature profile is visible at the melting interface throughout the charge cycle. At 8 h, the wax in the container is almost completely melted. Therefore, 8 h was chosen as the benchmark charge time to compare nanofluid PCM storage performance. The total enthalpy stored after 8 h is calculated through numerical integration of the nodal enthalpy values along the radius of the annulus. Total enthalpy was calculated for nanofluid PCMs with particle diameters ranging from 10 nm to 1 lm, at 0% to 2% volume fractions. As shown in Fig. 8(b), total stored enthalpy values are normalized relative to pure paraffin, and plotted with respect to particle volume fraction. Fig. 8(a) shows the temperature profile and progression of the melting front along the radius of the container. The horizontal line represents the melting temperature of pure paraffin. Fig. 8(b) compares the energy stored in the nanofluid system at the end of 8 h for different particle concentrations and sizes. The results show that the addition of highly conductive, micro-scale particles increases storage capacity relative to pure paraffin. However, for nanoscale inclusions, the enhancement in thermal conductivity is less significant than the reduction in latent heat of fusion, and

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Table 2 Equations to calculate temperature, liquid volume fraction k, and thermal conductivity, based on ranges of nodal enthalpy values. The three ranges of enthalpies signify material in solid, partial mush, and liquid state. Ti+1 j

Solver condition 06

Eiþ1 j

< qcs ðT melt  T init Þ

qcs ðT melt  T init Þ 6

Eiþ1 j

< qcs ðT melt  T init Þ þ qhsl

qcs ðT melt  T init Þ þ qhsl 6 Eiþ1 j

Eiþ1 j

T init þ qcs Tmelt

Nanoparticle: Multi-walled carbon nanotubes Thermal conductivity [28] Kapitza resistance Bulk medium: Paraffin wax Thermal conductivity [3] Density [3] Specific heat capacity Latent heat of fusion Melting temperature

21 W/m K 1  108 Km2/W 0.21 W/m K (solid) 0.12 W/m K (liquid) 900 kg/m3 (solid) 780 kg/m3 (liquid) 1888 J/kg K (solid) 2272 J/kg K (liquid) 1.8  105 J/kg 326 K

energy storage capacity is decreased over the PCM charge period. The reduction in storage performance is more severe as particle size decreases. With 10 nm particles, the relative energy stored is less than that of pure paraffin. These results suggest that the nanofluid approach is not an effective method for increasing PCM thermal storage performance. Although larger nanofluid particle diameters exhibit enhanced storage performance, the benefits may be negligible when considering cost and manufacturability, increased viscosity, and long term suspension stability. However, since the model parameters are dependent on material properties such as aspect ratio and interfacial resistance, storage performance may differ with the nanofluid materials selected. Additional studies are needed to fully understand the mechanisms of latent heat reduction.

ki+1 j

0

ks

Eiþ1 qcs ðT melt T init Þ j qhsl

Eiþ1 qðhsl cs T init cl T melt Þ j qðcs þcl Þ

Table 3 Physical and thermal properties of multi-walled carbon nanotubes and paraffin wax applied to the numerical model of a nanofluid PCM storage container undergoing a charge cycle.

ki+1 j

1



kiþ1 j kl T melt

1kiþ1

þ ks T j

1

melt

kl

4. Conclusions The latent heat of fusion of paraffin-based nanofluids containing multi-walled carbon nanotubes (MWNTs) has been investigated, utilizing differential scanning calorimetry (DSC). The latent heat of fusion of nanofluid samples containing various diameter multi-walled nanotubes was observed to reduce below theoretical expectations. The rate of nanofluid latent heat reduction, with respect to particle volume fraction, was shown to increase in magnitude with smaller diameter nanoparticles in suspension. Interfacial phenomena such as interfacial liquid layering, Brownian motion, and particle clustering were proposed as reduction mechanisms and explored with respect to measured results. It is concluded that Brownian motion and liquid layering are incapable of solely accounting for the degree of latent heat reduction observed. Particle clustering is demonstrated as a potential mechanism for latent heat reduction, but further investigation is needed. The effect of latent heat reduction on nanofluid PCM thermal energy storage performance was also presented. Defining storage performance as the amount of heat stored or extracted over a given duration, our previous work showed that nanofluids of smaller particle diameter can theoretically improve storage performance. There is a limit, however, to the practicality of reduced specific storage capacity. Although more heat is transferred at a faster rate, larger volumes of phase change material (PCM) are needed to account for the reduced amount of energy stored per unit mass. A onedimensional finite element model of nanofluid phase change in an annular storage container was presented as a predictive tool to assess diameter-dependent nanofluid storage performance. Based on the enthalpy method, discretized equations and boundary conditions were derived from the first law of thermodynamics to calculate internal energy at iterative time steps. The development

Fig. 8. (a) Temperature distribution along the radius of the annulus at different time intervals. (b) Total enthalpy saved after an 8 h charge cycle, normalized relative to pure paraffin.

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of a governing tridiagonal matrix is shown, including equations to calculate temperature and material phase at each node within the finite element mesh. The numerical model shows that while the addition of micro-scale particle increases thermal storage performance, nanoscale inclusions are shown to degrade storage performance relative to pure paraffin. With smaller particles, the beneficial effect of thermal conductivity enhancement is negated by significant reduction in latent heat of fusion, resulting in less energy stored over a given charge period. These results suggest that the nanofluid approach is not an effective method for improving PCM thermal storage performance, and may not be justifiable for thermal storage applications. However, these results are confined to the material properties of the system observed, and storage performance may vary depending on the nanofluid materials used. Conflict of interest None declared. Acknowledgments This work was supported by the School of Engineering, Sustainability Initiative Grant, and the Center for Science, Technology, and Society at Santa Clara University. The authors would like to acknowledge Bernadette Tong for her valuable comments during revisions. References [1] W. Wu, H. Bostanci, L.C. Chow, Y. Hong, C.M. Wang, M. Su, J.P. Kizito, Heat transfer enhancement of PAO in microchannel heat exchanger using nanoencapsulated phase change indium particles, Int. J. Heat Mass Transfer 58 (1– 2) (2013) 348–355. [2] H. Zhang, X. Wang, D. Wu, Silica encapsulation of n-octadecane via sol–gel process: a novel microencapsulated phase-change material with enhanced thermal conductivity and performance, J. Colloid Interface Sci. 343 (1) (2010) 246–255. [3] J. Fukai, Y. Hamada, Y. Morozumi, O. Miyatake, Improvement of thermal characteristics of latent heat thermal energy storage units using carbon-fiber brushes: experiments and modeling, Int. J. Heat Mass Transfer 46 (23) (2003) 4513–4525. [4] R. Velraj, R.V. Seeniraj, B. Hafner, C. Faber, K. Schwarzer, Heat transfer enhancement in a latent heat storage system, Sol. Energy 65 (3) (1999) 171– 180. [5] P. Keblinski, J. Eastman, D. Cahill, Nanofluids for thermal transport, Mater. Today 8 (6) (2005) 36–44. [6] C. Kleinstreuer, Y. Feng, Experimental and theoretical studies of nanofluid thermal conductivity enhancement: a review, Nanoscale Res. Lett. 6 (1) (2011) 229.

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